A Comparative Study Of Shu, Suanshushu And Nine Chapters

This thesis compares the representative questions in bamboo strips Shu《数》, Suanshushu《算数书》 and classic Nine Chapters《九章算术》, such as geometry, Yingbuzu盈不足, allocationaccording to the position and status, levy and estimation of construction, etc. And it analyzes thesimilarities and differences in the object of the processing, the question expression and methods ofthese texts. The author finds that, compared with other kinds of mathematical problems, the wayof solving the geometry question is more abstract, and the method, or the so-called shu术, is moreindependent of the counting of numbers. It is especially prominent in Shu, which is the earliestdocument. The mathematical expressions in Nine Chapters are more formal than those in others.The Nine Chapters avoids the omitted expressions in the bamboo strips and applies more accuratemethods. In addition, in the process of editing Nine Chapters, we cannot say the two bamboostrips are direct references for Nine Chapters, which only has the same source with them inmathematics.The potentiality of wide use and the prominence of characteristic of typical Yingbuzu hadbeen recognized in Nine Chapters rather than Shu or Suanshushu. Besides, terms in Yingbuzu inbamboo strips are identical with numerator and denominator in fraction. This reflects that the birthof Yinbuzu has a close relationship with the concept and operation of fraction. And we also findthat ancient people were very prudent when using this method. They probably made hypothesesand checked their calculation many times to get correct answers.More importantly, when we compare it with the two bamboo strips, Nine Chapters, whichhas long been treated as a research focus in studying of mathematics, reflects some characteristicswhich have once been ignored. Apart from more accurate terms, more rigorous treatment of dataand more complete methods, Nine Chapters embraced broader background of the questions and more complex thoughts of system design. This means that on the practical orientation of Chinesetraditional mathematics, more layers are differentiated. Mathematics, as an instrumental reason,had been used to a great extent to construct and assure the justice and rationality of a policy thenin Nine Chapters. It embodies the bureaucratic property of “solving big issue and developing lotsof manpower and resources”, particularly in the following aspects, such as the scale of the project,the number of people involved, the complex realistic factors, etc. This kind of property could notbe involved with the junior officers. So we say that in the development of early Chinesemathematics, there is a new perspective which regards Nine Chapters as the representative of“Bureaucratic Mathematics” and the bamboo strips as “Daily Arithmetic”. The differences ofthese literatures could not only be distinguished according to the difficulty of the questions, andthe differences are more distinct from the new respective.